Mixing
Is derivations of terms in series is equal to series of terms derivations?
$begingroup$
If $a_n(z)=log(b_n(z))$, such that
$b_n(z)=u_{k}(x)+ i v_{k}(x)$ is an analytic one-variable complex function and differentiable,
in which conditions on $a_n(z)$ in complex analysis, if $f(z)=lim_{nto infty}sum_{k=1}^{infty}a_{n}(z)$, then $f'(z)=lim_{nto infty}sum_{k=1}^{infty}a'_{n}(z)$?
sequences-and-series complex-analysis derivatives
edited Jan 29 at 15:43
J. W. Tanner
4,0961320
asked Jan 29 at 8:34
Jamal FarokhiJamal Farokhi
454210
$endgroup$
add a comment |
$begingroup$
If $a_n(z)=log(b_n(z))$, such that
$b_n(z)=u_{k}(x)+ i v_{k}(x)$ is an analytic one-variable complex function and differentiable,
in which conditions on $a_n(z)$ in complex analysis, if $f(z)=lim_{nto infty}sum_{k=1}^{infty}a_{n}(z)$, then $f'(z)=lim_{nto infty}sum_{k=1}^{infty}a'_{n}(z)$?
sequences-and-series complex-analysis derivatives
edited Jan 29 at 15:43
J. W. Tanner
4,0961320
asked Jan 29 at 8:34
Jamal FarokhiJamal Farokhi
454210
$endgroup$
$begingroup$
$a_n$ does not depend on $n$, maybe you made a typo
$endgroup$
– Leonardo
Jan 29 at 16:33
add a comment |
$begingroup$
If $a_n(z)=log(b_n(z))$, such that
$b_n(z)=u_{k}(x)+ i v_{k}(x)$ is an analytic one-variable complex function and differentiable,
in which conditions on $a_n(z)$ in complex analysis, if $f(z)=lim_{nto infty}sum_{k=1}^{infty}a_{n}(z)$, then $f'(z)=lim_{nto infty}sum_{k=1}^{infty}a'_{n}(z)$?
sequences-and-series complex-analysis derivatives
edited Jan 29 at 15:43
J. W. Tanner
4,0961320
asked Jan 29 at 8:34
Jamal FarokhiJamal Farokhi
454210
$endgroup$
If $a_n(z)=log(b_n(z))$, such that
$b_n(z)=u_{k}(x)+ i v_{k}(x)$ is an analytic one-variable complex function and differentiable,
in which conditions on $a_n(z)$ in complex analysis, if $f(z)=lim_{nto infty}sum_{k=1}^{infty}a_{n}(z)$, then $f'(z)=lim_{nto infty}sum_{k=1}^{infty}a'_{n}(z)$?
sequences-and-series complex-analysis derivatives
sequences-and-series complex-analysis derivatives
edited Jan 29 at 15:43
J. W. Tanner
4,0961320
asked Jan 29 at 8:34
Jamal FarokhiJamal Farokhi
454210
edited Jan 29 at 15:43
J. W. Tanner
4,0961320
asked Jan 29 at 8:34
Jamal FarokhiJamal Farokhi
454210
edited Jan 29 at 15:43
J. W. Tanner
4,0961320
edited Jan 29 at 15:43
J. W. Tanner
4,0961320
edited Jan 29 at 15:43
J. W. Tanner
4,0961320
4,0961320
asked Jan 29 at 8:34
Jamal FarokhiJamal Farokhi
454210
asked Jan 29 at 8:34
Jamal FarokhiJamal Farokhi
454210
asked Jan 29 at 8:34
Jamal FarokhiJamal Farokhi
454210
454210
$begingroup$
$a_n$ does not depend on $n$, maybe you made a typo
$endgroup$
– Leonardo
Jan 29 at 16:33
add a comment |
$begingroup$
$a_n$ does not depend on $n$, maybe you made a typo
$endgroup$
– Leonardo
Jan 29 at 16:33
$begingroup$
$a_n$ does not depend on $n$, maybe you made a typo
$endgroup$
– Leonardo
Jan 29 at 16:33
$begingroup$
$a_n$ does not depend on $n$, maybe you made a typo
$endgroup$
– Leonardo
Jan 29 at 16:33
add a comment |
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$begingroup$
$a_n$ does not depend on $n$, maybe you made a typo
$endgroup$
– Leonardo
Jan 29 at 16:33